Найдите неопределенный интеграл:[latex] \int\limits \frac{dx}{sin^2xcos^2x}[/latex]

[latex] \int \dfrac{dx}{\sin^2x\cos^2x}= \int \dfrac{1}{\sin^2x\cos^2x}dx= \int \dfrac{\sin^2x+\cos^2x}{\sin^2x\cos^2x}dx= \\\\\ = \int \dfrac{\sin^2x}{\sin^2x\cos^2x}dx+\int \dfrac{\cos^2x}{\sin^2x\cos^2x}dx= \int \dfrac{1}{\cos^2x}dx+\int \dfrac{1}{\sin^2x}dx= \\\\\ =\mathrm{tg}x-\mathrm{ctg}x+C[/latex]